Solution: The LCM of 50 and 136 is 3400
Methods
How to find the LCM of 50 and 136 using Prime Factorization
One way to find the LCM of 50 and 136 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 50?
What are the Factors of 136?
Here is the prime factorization of 50:
2
1
×
5
2
2^1 × 5^2
2 1 × 5 2
And this is the prime factorization of 136:
2
3
×
1
7
1
2^3 × 17^1
2 3 × 1 7 1
When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 2, 5, 17
2
3
×
5
2
×
1
7
1
=
3400
2^3 × 5^2 × 17^1 = 3400
2 3 × 5 2 × 1 7 1 = 3400
Through this we see that the LCM of 50 and 136 is 3400.
How to Find the LCM of 50 and 136 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 50 and 136 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.
Let’s take a look at the multiples for each of these numbers, 50 and 136:
What are the Multiples of 50?
What are the Multiples of 136?
Let’s take a look at the first 10 multiples for each of these numbers, 50 and 136:
First 10 Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, 500
First 10 Multiples of 136: 136, 272, 408, 544, 680, 816, 952, 1088, 1224, 1360
You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 50 and 136 are 3400, 6800, 10200. Because 3400 is the smallest, it is the least common multiple.
The LCM of 50 and 136 is 3400.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 8 and 52?
What is the LCM of 128 and 27?
What is the LCM of 140 and 83?
What is the LCM of 31 and 19?
What is the LCM of 91 and 58?